Well, there's the general idea of the Butterfly effect in General which could lead to slightly different military situations in the Balkans,
A different winner in 1912 US presidential election would not change the situation in the Balkins, unless TR successfully negotiates a peace treaty. I doubt he would be all that interested in events in the Balkins. Even if there is no Balkan War, Austria Hungary does not turn Bosnia over to Serbia. Therefore Franz Ferdiand still comes to Sarajevo and the Black Hand still wants to kill him.